Initial Commit

Common/BezierBuilder.cs

@@ -0,0 +1,120 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Windows;
+
+namespace Microsoft.Research.DynamicDataDisplay.Charts.NewLine
+{
+	// todo check a license
+	public static class BezierBuilder
+	{
+		public static IEnumerable<Point> GetBezierPoints(Point[] points)
+		{
+			if (points == null)
+				throw new ArgumentNullException("points");
+
+			Point[] firstControlPoints;
+			Point[] secondControlPoints;
+
+			int n = points.Length - 1;
+			if (n < 1)
+				throw new ArgumentException("At least two knot points required", "points");
+			if (n == 1)
+			{ // Special case: Bezier curve should be a straight line.
+				firstControlPoints = new Point[1];
+				// 3P1 = 2P0 + P3
+				firstControlPoints[0].X = (2 * points[0].X + points[1].X) / 3;
+				firstControlPoints[0].Y = (2 * points[0].Y + points[1].Y) / 3;
+
+				secondControlPoints = new Point[1];
+				// P2 = 2P1 – P0
+				secondControlPoints[0].X = 2 *
+					firstControlPoints[0].X - points[0].X;
+				secondControlPoints[0].Y = 2 *
+					firstControlPoints[0].Y - points[0].Y;
+
+				return Join(points, firstControlPoints, secondControlPoints);
+			}
+
+			// Calculate first Bezier control points
+			// Right hand side vector
+			double[] rhs = new double[n];
+
+			// Set right hand side X values
+			for (int i = 1; i < n - 1; ++i)
+				rhs[i] = 4 * points[i].X + 2 * points[i + 1].X;
+			rhs[0] = points[0].X + 2 * points[1].X;
+			rhs[n - 1] = (8 * points[n - 1].X + points[n].X) / 2.0;
+			// Get first control points X-values
+			double[] x = GetFirstControlPoints(rhs);
+
+			// Set right hand side Y values
+			for (int i = 1; i < n - 1; ++i)
+				rhs[i] = 4 * points[i].Y + 2 * points[i + 1].Y;
+			rhs[0] = points[0].Y + 2 * points[1].Y;
+			rhs[n - 1] = (8 * points[n - 1].Y + points[n].Y) / 2.0;
+			// Get first control points Y-values
+			double[] y = GetFirstControlPoints(rhs);
+
+			// Fill output arrays.
+			firstControlPoints = new Point[n];
+			secondControlPoints = new Point[n];
+			for (int i = 0; i < n; ++i)
+			{
+				// First control point
+				firstControlPoints[i] = new Point(x[i], y[i]);
+				// Second control point
+				if (i < n - 1)
+					secondControlPoints[i] = new Point(2 * points
+						[i + 1].X - x[i + 1], 2 *
+						points[i + 1].Y - y[i + 1]);
+				else
+					secondControlPoints[i] = new Point((points
+						[n].X + x[n - 1]) / 2,
+						(points[n].Y + y[n - 1]) / 2);
+			}
+
+			return Join(points, firstControlPoints, secondControlPoints);
+		}
+
+		private static IEnumerable<Point> Join(Point[] points, Point[] firstControlPoints, Point[] secondControlPoints)
+		{
+			var length = firstControlPoints.Length;
+			for (int i = 0; i < length; i++)
+			{
+				yield return points[i];
+				yield return firstControlPoints[i];
+				yield return secondControlPoints[i];
+			}
+
+			yield return points[length];
+		}
+
+		/// <summary>
+		/// Solves a tridiagonal system for one of coordinates (x or y)
+		/// of first Bezier control points.
+		/// </summary>
+		/// <param name="rhs">Right hand side vector.</param>
+		/// <returns>Solution vector.</returns>
+		private static double[] GetFirstControlPoints(double[] rhs)
+		{
+			int n = rhs.Length;
+			double[] x = new double[n]; // Solution vector.
+			double[] tmp = new double[n]; // Temp workspace.
+
+			double b = 2.0;
+			x[0] = rhs[0] / b;
+			for (int i = 1; i < n; i++) // Decomposition and forward substitution.
+			{
+				tmp[i] = 1 / b;
+				b = (i < n - 1 ? 4.0 : 3.5) - tmp[i];
+				x[i] = (rhs[i] - x[i - 1]) / b;
+			}
+			for (int i = 1; i < n; i++)
+				x[n - i - 1] -= tmp[n - i] * x[n - i]; // Backsubstitution.
+
+			return x;
+		}
+	}
+}